we have for quadratic equations x=((−b±(√(b^2 −4ac)))/(2a)) what about cubic equation is there any rules or ways to solve?


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Question Number 93963 by M±th+et+s last updated on 16/May/20

$w e h a v e f o r q u a d r a t i c e q u a t i o n s$ $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $w h a t a b o u t c u b i c e q u a t i o n i s t h e r e a n y$ $r u l e s o r w a y s t o s o l v e ?$
Commented by Kunal12588 last updated on 16/May/20

$f o r t h e r o o t s I h e a r d t h e r e i s a f o r m u l a f o r$ $c u b i c t o o b u t i t i s t o o l o n g t o b e r e m e m b e r e d .$ $s a m e f o r b i q u a d r a t i c . [{d o n}^{'} t k n o w f o r h i g h e r]$ $b u t t h e r e a r e m e t h o d s t o s o l v e l i k e c a r d a n o a n d$ $t r i g o n o m e t r i c [I h e a r d o f F a r r a r i t o o, I t h i n k$ ${i t}^{'} s f o r b i q u a d r a t i c]$
Commented by mr W last updated on 16/May/20

$s e e Q 89687$
Commented by mr W last updated on 16/May/20

$o n c e i m a d e f o l l o w i n g s u m m a r y f o r$ $c u b i c e q u a t i o n :$
Commented by mr W last updated on 16/May/20

Commented by M±th+et+s last updated on 16/May/20

$t h a n k y o u s i r$
Commented by Tony Lin last updated on 16/May/20

Commented by Tony Lin last updated on 16/May/20

Commented by Tony Lin last updated on 16/May/20

Commented by Tony Lin last updated on 16/May/20

$w e s t i l l c a n g e t t h e f o r m u l a o f c u b i c$ $a n d b i q u a d r a t i c i n t e r m s o f a, b, c, d, e$ $b u t t h e y a r e t o o h a r d t o r e m e m b e r,$ $w h i c h i s t o t a l l y n o t u s e f u l$
Commented by M±th+et+s last updated on 16/May/20

$t h a n k y o u s i r$
Commented by M±th+et+s last updated on 16/May/20

$s i r M R . W c a n y o u p u t a n e x a m p l e f o r t h i s r u l e$ $a n d t h a n k y o u a g a i n$
Commented by mr W last updated on 16/May/20

$y o u c a n a p p l y t h e f o r m u l a e d i r e c t l y$ $f o r a n y c u b i c e q u a t i o n, i {d o n}^{'} t t h i n k$ $y o u n e e d a n e x a m p l e . b u t i g i v e a n$ $e x a m p l e :$ $x^{3} - 3 x - 4 = 0$ $p = - 1, q = - 2$ $p^{3} + q^{2} = - 1 + 4 = 3 > 0 \Rightarrow o n e r e a l r o o t$ $x = \sqrt[3]{\sqrt{3} + 2} - \sqrt[3]{\sqrt{3} - 2} \approx 2.1958$
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